Very confused

You describe this:    5x  = 5 + x 

                                  4x = 5

                                    x = 5/4    ( the other number )

 

Noah was asked to compute the product of two numbers. He misread the problem and entered the sum of the two numbers instead. Luckily he still got the right answer. One of the two numbers is 5. What is the other number?    

5 is one number  

x is the other number  

 

Noah got the right answer.  That means you get the same answer either way.  So....   5 • x  =  5 + x  

 

                                                  5x  =  5 + x    

 

Subtract x from both sides         5x – x  =  5   

 

                                                    4x  =  5   

 

Divide both sides by 4                   x  =  5/4     or, if you prefer it in decimal form, 1.25  

_.

5 + x = 5x -> 5 = 4x -> divide by 4 -> 5/4 = x. 

                So x = 5/4